Multiple colors per vertex
That looks to me like you have a few overlapping faces. The give-away is that there's some shimmering (called "z-fighting") going on between unpainted white vertices and the yellow verts.

With Vertex Painting you can limit the faces using a Mask. Any unmasked faces will receive no vertex paint instructions.



This masking mode lets you right click faces to select (mask) them: 


then pick your colors (from the left panel), 
move mouse close to the vertex you want to color 
left click to color.


The vertex paint page in the manual is worth reading for all the options.

Shift+K is great for giving all masked faces the same color instantly. Notice that all masked edges get a faint dotted line around their perimeter.